arXiv 1502.045102015-02math.AG

The maximum number of lines lying on a K3 quartic surface

Davide Cesare Veniani

备注：: 31 pages, 3 tables, 1 figure
发表信息：: Math. Z. 285 (2017), no. 3, 1141--1166
DOI：: 10.1007/s00209-016-1742-6

英文摘要：

We show that there cannot be more than 64 lines on a quartic surface admitting isolated rational double points over an algebraically closed field of characteristic $p \neq 2,\,3$, thus extending Segre--Rams--Schütt theorem. Our proof offers a deeper insight into the triangle-free case and takes advantage of a special configuration of lines, thereby avoiding the technique of the flecnodal divisor. We provide several examples of non-smooth K3 quartic surfaces with many lines.

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